Ansys analysis of weakly magnetic materials in MR tomography

Ansys analysis o weakly magne ic ma e ials in MR omog aphy 15 ANSYS ANALYSIS OF WEAKLY MAGNETIC MATERIALS IN MR TOMOGRAPHY Milosla S einbaue *, Ka el Ba usek ** *Facul y o Elec ical Enginee ing and Communica ion, B no Uni e si y o Technology, Pu kyo a 464/118, 612 00 B no, Czech Republic, s einbau@ eec. u b .cz **Ins i u e o Scien i ic Ins umen s, Academy o Sciences o he Czech Republic, K alo opolská 147, 612 00 B no, Czech Republic, ba @isib no.cz Summa y The pape deals wi h he impac o weakly magne ic ma e ials on magne ic ield in MR omog aphy. The esul s ob ained by ini e elemen me hod modelling as well as da a measu ed by MR omog aphy a e in oduced. Me hod o magne ic suscep ibili y de e mina ion using MRI is discussed. 1. INTRODUCTION Basic ield homogenei y is one o he p incipal equi emen s in MR omog aphy. P esence o magne ic ma e ials in measu ed specimen b ings abou local pe u ba ion o his ield, which esul s in de o ma ion o cap u ed image. Because o high equi ed homogenei y (10 -6 and be e ), al eady ma e ials wi h e y low suscep ibili y ha e signi ican impac . Because o possibili y o u u e elimina ion o a e ac in MR images caused by such ma e ials, knowledge o ma e ial suscep ibili y is e y impo an . Fo example, p esence o den al illing, when an MR image o head is made, b ings ou local loss o pic u e in o ma ion. Fig. 1 Impac o pa amagne ic specimen on MR ield homogenei y Measu emen o suscep ibili y can be ealized by se e al me hods. One me hod based on low- equency induc i e b idge wi h ield in ensi y abou 300 A/m was de eloped by AGICO Company [5], [6]. Achie ed sensi i i y o his me hod allows measu emen o ma e ial wi h suscep ibili y o o de 10 -5 , mo eo e magne ic aniso opy can be obse ed. Magne ic esonance e ec b ings ano he possibili y o suscep ibili y e alua ion. P inciple o measu emen is elemen a y o ma e ials which gi es signal in MR omog aphy. When sui able imaging me hod is applied (usually g adien echo – GE), in o ma ion abou local change o magne ic induc ion o ield in sample is phase-coded in ob ained image. F om known shape o induc ion, local alue o pe meabili y µ o suscep ibili y χ can be de i ed using Laplace's equa ion m 0 ϕ ∆ = (1) One o me hods o suscep ibili y measu emen o ma e ials, which gi es no MR signal, was desc ibed in [1]. This me hod uses compa ison wi h e e ence ma e ials o known χ (such as wa e , ace one, …). Because no signal o m inside a ea is acqui ed and hus change o magne ic induc ion inside i can’ be enume a ed, he induc ion in specimen icini y is an objec o in e es . Below in his pape we will discuss measu ing echnique, which is sui able o subs ances wi h no signal in MR omog aphy. Fo illus a ion see Fig. 1, whe e is shown slice o MR expe imen model wi h specimen o suscep ibili y 4 S 1 10 χ − = ⋅ in basic ield wi h magne ic induc ion 0 4.700 T B =. De o ma ion o magne ic induc ion ield in specimen a i e, mo eo e ield in specimen icini y is a ec ed. This igu e has been ob ained om Ansys model Fig. 3 below. 2. PRINCIPLE OF THE METHOD The me hod is based on cons an magne ic lux in wo king space o supe conduc ing magne . Inse ing o he specimen o hickness ∆x and wi h magne ic suscep ibili y χ s causes local de o ma ion o homogeneous magne ic ield (idealized case is in Fig. 2) ( ) s 0 s 1 B B χ = ⋅ + . (2) Assume cons an magne ic lux Φ  h u no mal a ea o c oss-sec ion S o he magne wo king space . S B dS cons φ = ⋅ =  (3) Suppose he specimen has enough la ge leng h in y -axes di ec ion, so we can neglec bounda y e ec . Fo z-x c oss-sec ion Fig. 2 in he middle o he specimen we can w i e ( ) 0 0 B x B dx ε ε − − ⋅ =      , (4) wha means ha sum o ha ched a eas bounded by cu e in Fig. 2 wi h espec o he base alue o induc ion B 0 is Ad ances in Elec ical and Elec onic Enginee ing 16 ze o, whe e ε is su icien dis ance om specimen wi h espec o i s impac on induc ion change. Fig. 2 Change o magne ic induc ion ield in pa amagne ic specimen and i s icini y – idealized case I we can de e mine he cou se o ( ) B x (using sui able MRI echnique and e e ence subs ance gi ing MR signal in su oundings o ma e ial), we can also enume a e B s and χs alues o he in es iga ed specimen ma e ial. F om p incipal case in Fig. 2 we can de i e: ( ) ( ) x 0 S 0 /2 2 x B x B dx B B ε ∆ − ⋅ ≅ ∆ −      , (5) and using (2) ( ) x 0 /2 S 0 2 x B x B dx B ε χ ∆ − ⋅     ≅∆ ⋅  . (6) Desc ibed me hod was nume ically modelled in Ansys and checked on 200 MHz MR omog aph in Ins i u e o Scien i ic Ins umen s, Academy o Sciences. 3. NUMERICAL MODELING a) b) Fig. 3 Geome ical and meshed model (cylind ical a angemen ) One o used Ansys 3D models is on Fig. 3 (a - geome ical model, b - meshed model). Volumes wi h di e en magne ic p ope ies ha e di e en colou . Nume ical modelling was p o ided using Ansys 6.1 so wa e. Using FEM he scala magne ic po en ial Φ m was compu ed by sol ing o Laplace’s equa ion (1). One o used model is in Fi . 4. The model was meshed wi h Solid96 elemen ype. Bounda y condi ions we e se up o achie e induc ion B 0 = 4,700 T in z -axes di ec ion: • . m cons Φ = on he su aces Γ1, Γ2, • 0 m n ∂Φ = ∂ on he shell su ace Γ3. Fig. 4 Simple Ansys model, dimensions a e in mm The module o magne ic induc ion B along he “pa h” ma ked in Fig. 4, ob ained by sol ing o men ioned model, is depic ed in Fig. 5. Fig. 5 Cou se o magne ic induc ion in sec ion o model in ig. 4 Ano he model, used o e i ica ion o suscep ibili y measu emen is in Fig. 6. He e weakly pa amagne ic specimen is su ounded by diamagne ic χs 160 160 pa h Γ1 Γ2 Γ3 z B(x) B 0 ∆x B s 2 x ∆ x ε Ansys analysis o weakly magne ic ma e ials in MR omog aphy 17 e e ence subs ance. Ob ained cou se o B in sec ion is in Fig. 7. In eal expe imen he e e ence ma e ial and he specimen a e sepa a ed wi h hin laye , e.g. cu e e wall. In model (Fig. 6) we conside ed 1 mm hick cu e e made om PE. Because polye hylene is pa amagne ic, li le peak occu s in g aph Fig. 7. Fig. 6 Magne ic induc ion ield p ojec ed on meshed model Fig. 7 Cou se o magne ic induc ion in sec ion o model in Fig. 6. Peak is caused due o PE cu e e 4. EXPERIMENTAL MEASUREMENT P esen ed me hod was expe imen ally e i ied wi h numbe o specimens on 200 MHz MR omog aph in ISI AS B no. Re e ence subs ance was wa e (χ H2O = -9.04·10 -6 ) illed in o cu e e. The me hod o G adien echo [3] was used o acqui e MR image wi h con as co esponding o he magne ic induc ion changes in measu ed olume o specimen icini y. Used measu ing sequence o GE is on Fig. 8. Exci a ion o hyd ogen nucleus p o ides HF pulse 90°, which d ops ec o o magne iza ion spin M 0 om di ec ion z (pa allel o B 0 ) o ans e sal plane x-y. Ene gy o his pulse causes phase-ma ching o nucleus spins. Du ing exci a ion, slice g adien G S alloca es measu ed specimen laye . Only his laye is exci ed and only om his laye he MR image is consequen ly acqui ed. Read-ou g adien G R causes coding o x- posi ion in o equency and a he same ime phase g adien G P causes coding o y-posi ion in o phase o esul MR signal. Spin-spin incidence and g adien ields induce lapse o phase-ma ching o magne iza ion ec o s, so e- ma ching o spins by ead-ou g adien in e sion is used. Signal acquisi ion is pe o med in echo ime TE a e exci a ion. Fig. 8 P inciple o g adien echo measu ing sequence One o GE me hod p ope y is i s sensi i i y on basic ield inhomogenei y and inhomogenei y induced by magne ic ma e ial in he specimen. GE MR image is phase-modula ed by magne ic induc ion change [2], [3] and on condi ion o p ope expe imen a angemen we can ob ain image o magne ic ield dis ibu ion in specimen icini y and inally enume a e specimen suscep ibili y (6). Fig. 9 Unw apped cu e o signal phase change in specimen icini y Using desc ibed GE me hod we ob ained MR image wi h phase-con as – Fig. 10 uppe , which was u he p ocessed in Ma lab. A e de-noising by he limi a ion o signal he spa ial de o ma ion e oked by magne ic ield inhomogenei y in specimen icini y was elimina ed. Acqui ed phase images we e consequen ly sub ac ed o elimina e inhomogenei y o he basic ield and unw apped ( his means discon inui ies in phase Ad ances in Elec ical and Elec onic Enginee ing 18 change be ween –π and π we e emo ed) – esul is on Fig. 10 lowe . By p ope ly selec ed slice o his image we ge he cu e o phase change Θ(x) o he wa e MR signal in he specimen icini y, see Fig. 9. Fig. 10 Images ob ained om expe imen al e i ica ion o he me hod, p ocessed in Ma lab Fo he used MR echnique he phase change Θ(x) esponse o he magne ic induc ion change ( ) ( ) 0 E x B x B T γ Θ = + ⋅, (7) whe e γ is gy omagne ic a io o wa e and T E = 5.56 ms was used echo- ime. In his way we can iden i y he cou se o magne ic induc ion change in wa e nea by he specimen. F om known hickness ∆ x o he specimen wi h use o (6) he suscep ibili y o specimens can be inally calcula ed. 5. CONCLUSION The me hod designed o magne ic suscep ibili y measu emen based on MR omog aphy echniques is simple and enables o de e mine he magne ic suscep ibili y o such ma e ials, which gi e no MR signal. P inciple o he me hod was designed using Ansys modelling and expe imen ally e i ied in labo a o y. A e an op imiza ion his me hod can be used o in es iga ion o he ma e ials used in MR omog aphy as well as o biological issues a ec ing quali y o MR images. ACKNOWLEDGEMENT This wo k has been pa ially unded by a g an GA  R 103/03/7048 and g an GAAV IAA2065201. LITERATURE [1] ZEMAN, V. M  ení magne ické suscep ibili y pomocí NMR. Tesla B no, in e ní zp á a, 1981 [2] BLUMLICH, B. NMR Imaging o Ma e ials. Cla en on P ess, Ox o d, 2000, ISBN 0 19 850683 X [3] ERNST, R. R. – BODENHAUSEN, G. – WOKAUN, A. P inciples o NMR in One and Two Dimensions. Ox o d Science Publ. 1987, ISBN 0- 198-55647-0 [4] LEVITT, M. H. Spin Dynamics: Basics o Nuclea Magne ic Resonance. John Wiley & Sons, 2001, ISBN: 0-471-48921-2 [5] HROUDA, F. A de e mina ion o he symme y o he e omagne ic mine al ab ic in ocks on he basis o he magne ic suscep ibili y aniso opy measu emen s. Ge l. Bei . Geophys., 82,1973, pp.390-396 [6] HROUDA, F. Magne oc ys alline aniso opy o ocks and massi e o es: a ma hema ical model s udy and i s ab ic implica ions. J. S uc . Geol., 2, 1980, pp.459-462